Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1999 CEMC Gauss (Grade 7) Problems"

(Created page with "= Part A: Each correct answer is worth 5 points = == Problem 1 == <math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math> [[1...")
 
 
(4 intermediate revisions by the same user not shown)
Line 2: Line 2:
  
 
== Problem 1 ==
 
== Problem 1 ==
 +
<math>1999 - 999 + 99</math> equals
  
−
<math>\text{(A)}\  \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 901 \qquad \text{(B)}\ 1099 \qquad \text{(C)}\ 1000 \qquad \text{(D)}\ 199 \qquad \text{(E)}\ 99 </math>
  
−
[[1998 CEMC Gauss (Grade 7) Problems/Problem 1|Solution]]
+
[[1999 CEMC Gauss (Grade 7) Problems/Problem 1|Solution]]
  
 
== Problem 2 ==
 
== Problem 2 ==
 +
The integer <math>287</math> is exactly divisible by
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 6 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 2|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 2|Solution]]
  
 
== Problem 3 ==
 
== Problem 3 ==
 +
Susan wants to place <math>35.5</math> kg of sugar in small bags. If each bag holds <math>0.5</math> kg, how many bags are needed?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 36 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 53 \qquad \text{(D)}\ 70 \qquad \text{(E)}\ 71 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 3|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 3|Solution]]
  
 
== Problem 4 ==
 
== Problem 4 ==
 +
<math>1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}</math> is equal to
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ \frac{15}{8} \qquad \text{(B)}\ 1\frac{3}{14} \qquad \text{(C)}\ \frac{11}{8} \qquad \text{(D)}\ 1\frac{3}{4} \qquad \text{(E)}\ \frac{7}{8} </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 4|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 4|Solution]]
  
 
== Problem 5 ==
 
== Problem 5 ==
 +
Which one of the following gives an odd integer?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 6^2 \qquad \text{(B)}\ 23-17 \qquad \text{(C)}\ 9\times 24 \qquad \text{(D)}\ 96\div 8 \qquad \text{(E)}\ 9\times 41 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 5|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 5|Solution]]
  
 
== Problem 6 ==
 
== Problem 6 ==
 +
In <math>\Delta ABC</math>, <math>\angle B = 72^{\circ}</math>. What is the sum, in degrees, of the other two angles?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 144 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 108 \qquad \text{(D)}\ 110 \qquad \text{(E)}\ 288 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 6|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 6|Solution]]
  
 
== Problem 7 ==
 
== Problem 7 ==
 +
If the numbers, <math>\frac{4}{5}</math>, <math>81\%</math>, and <math>0.801</math> are arranged from smallest to largest, the correct order is
  
−
<math>\text{(A)}\ \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ \frac{4}{5}, 81\%, 0.801 \qquad \text{(B)}\ 81\%, 0.801, \frac{4}{5} \qquad \text{(C)}\ 0.801, \frac{4}{5}, 81\% \qquad \text{(D)}\ 81\%, \frac{4}{5}, 0.801 \qquad \text{(E)}\ \frac{4}{5}, 0.801, 81\%</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 7|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 7|Solution]]
  
 
== Problem 8 ==
 
== Problem 8 ==
 +
The average of <math>10</math>, <math>4</math>, <math>8</math>, <math>7</math>, and <math>6</math> is
  
−
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 33 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ </math> 7
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 8|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 8|Solution]]
  
 
== Problem 9 ==
 
== Problem 9 ==
 +
André is hiking on the paths shown in the map. He is planning to visit sites A to M in alphabetical order. He can never retrace his steps and he must proceed directly from one site to the next. What is the largest number of labelled points he can visit before going out of alphabetical order?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 6 \qquad \text{(B)}\ 7 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 13</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 9|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 9|Solution]]
  
 
== Problem 10 ==
 
== Problem 10 ==
 +
In the diagram, line segments meet at <math>90^{\circ}</math> as shown. If the short line segments are each <math>3</math> cm long, what is the area of the shape?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 30 \qquad \text{(B)}\ 36 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 45 \qquad \text{(E)}\ 54</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 10|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 10|Solution]]
Line 64: Line 74:
  
 
== Problem 11 ==
 
== Problem 11 ==
 +
The floor of a rectangular room is covered with square tiles. The room is 10 tiles long and 5 tiles wide. The number of tiles that touch the walls of the room is
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 26 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 46 \qquad \text{(E)}\ 50 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 11|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 11|Solution]]
  
 
== Problem 12 ==
 
== Problem 12 ==
 +
Five students named Fred, Gail, Henry, Iggy, and Joan are seated around a circular table in that order. To decide who goes first in a game, they play "countdown". Henry starts by saying "34", with Iggy saying "33". If they continue to count down in their circular order, who will eventually say "1"?
  
−
<math>\text{(A)}\  \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ Fred \qquad \text{(B)}\ Gail \qquad \text{(C)}\ Henry \qquad \text{(D)}\ Iggy \qquad \text{(E)}\ Joan </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 12|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 12|Solution]]
  
 
== Problem 13 ==
 
== Problem 13 ==
 +
In the diagram, the percent of small squares that are shaded is
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 9 \qquad \text{(B)}\ 33 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 56.25 \qquad \text{(E)}\ 64</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 13|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 13|Solution]]
  
 
== Problem 14 ==
 
== Problem 14 ==
 +
Which of the following is an odd integer, contains the digit <math>5</math>, is divisible by <math>3</math>, and lies between <math>12^2</math> and <math>13^2</math>?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 105 \qquad \text{(B)}\ 147 \qquad \text{(C)}\ 156 \qquad \text{(D)}\ 165 \qquad \text{(E)}\ 175 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 14|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 14|Solution]]
  
 
== Problem 15 ==
 
== Problem 15 ==
 +
A box contains <math>36</math> pink, <math>18</math> blue, <math>9</math> green, <math>6</math> red, and <math>3</math> purple cubes that are identical in size. If a cube is selected at random, what is the probability that it is green?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ \frac{1}{9} \qquad \text{(B)}\ \frac{1}{8} \qquad \text{(C)}\ \frac{1}{5} \qquad \text{(D)}\ \frac{1}{4} \qquad \text{(E)}\ \frac{9}{70} </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 15|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 15|Solution]]
  
 
== Problem 16 ==
 
== Problem 16 ==
 +
The graph shown at the right indicates the time taken by five people to travel various distances. On average, which person travelled the fastest?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ Alison \qquad \text{(B)}\ Bina \qquad \text{(C)}\ Curtis \qquad \text{(D)}\ Daniel \qquad \text{(E)}\ Emily</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 16|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 16|Solution]]
  
 
== Problem 17 ==
 
== Problem 17 ==
 +
In a "Fibonacci" sequence of numbers, each term beginning with the third, is the sum of the previous two terms. The first number in such a sequence is <math>2</math>, and the third term is <math>9</math>. What is the eighth term in the sequence?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 34 \qquad \text{(B)}\ 36 \qquad \text{(C)}\ 107 \qquad \text{(D)}\ 152 \qquad \text{(E)}\ 245 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 17|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 17|Solution]]
  
 
== Problem 18 ==
 
== Problem 18 ==
 +
The results of the hair colour of <math>600</math> people are shown in this circle graph. How many people have blonde hair?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 30 \qquad \text{(B)}\ 160 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 200 \qquad \text{(E)}\ 420</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 18|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 18|Solution]]
  
 
== Problem 19 ==
 
== Problem 19 ==
−
 
+
What is the area, in <math>m^2</math>, of the shaded part of the rectangle?
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 14 \qquad \text{(B)}\ 28 \qquad \text{(C)}\ 33.6 \qquad \text{(D)}\ 56 \qquad \text{(E)}\ 42 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 19|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 19|Solution]]
  
 
== Problem 20 ==
 
== Problem 20 ==
 +
The first 9 positive odd integers are placed in the magic square so that the sum of the numbers in each row, column and diagonal are equal. Find the value of A + E.
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 32 \qquad \text{(B)}\ 28 \qquad \text{(C)}\ 26 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 16</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 20|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 20|Solution]]
Line 126: Line 145:
  
 
== Problem 21 ==
 
== Problem 21 ==
 +
A game is played on the board. In this game, the player can move three places in any direction (up, down, right or left) and then can move two places in a direction perpendicular to the first move. If a player starts on S, which position on the board (P, Q, R, T, or W) cannot be reached through any sequence of moves?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ P \qquad \text{(B)}\ Q \qquad \text{(C)}\ R \qquad \text{(D)}\ T \qquad \text{(E)}\ W</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 21|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 21|Solution]]
  
 
== Problem 22 ==
 
== Problem 22 ==
 +
Forty-two cubes with <math>1</math> cm edges are glued together to form a solid rectangular block. If the perimeter of the base of the block is <math>18</math> cm, then the height, in cm, is
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ \frac{7}{3} \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 22|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 22|Solution]]
  
 
== Problem 23 ==
 
== Problem 23 ==
 +
<math>JKLM</math> is a square. Points P and Q are outside the square such that triangles JMP and MLQ are equilateral. The size, in degrees, of angle <math>PQM</math> is
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 10 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 25 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 150</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 23|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 23|Solution]]
  
 
== Problem 24 ==
 
== Problem 24 ==
 +
Five holes of increasing size are cut along the edge of one face of a box as shown. The number of points scored when a marble is rolled through that hole is the number above the hole. There are three sizes of marbles: small, medium and large. The small marbles  fit through any of the holes, the medium fit only through holes 3, 4, and 5, and the large fit only through hole 5. You may choose up to 10 marbles of each size to roll and each rolled marble goes through a hole. For a score of 23, what is the maximum number of marbles that could have been rolled?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 12 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 14 \qquad \text{(D)}\ 15 \qquad \text{(E)}\ 16 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 24|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 24|Solution]]
  
 
== Problem 25 ==
 
== Problem 25 ==
 +
In a softball league, after each team has played every other team 4 times, the total accumulated points are: Lions 22, Tigers 19, Mounties 14, and Royals 12. If each team received 3 points for a win, 1 point for a tie and no points for a loss, how many games ended in a tie?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 10</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 25|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 25|Solution]]

Latest revision as of 10:10, 15 April 2025

Part A: Each correct answer is worth 5 points

Problem 1

$1999 - 999 + 99$ equals

$\text{(A)}\ 901 \qquad \text{(B)}\ 1099 \qquad \text{(C)}\ 1000 \qquad \text{(D)}\ 199 \qquad \text{(E)}\ 99$

Solution

Problem 2

The integer $287$ is exactly divisible by

$\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 6$

Solution

Problem 3

Susan wants to place $35.5$ kg of sugar in small bags. If each bag holds $0.5$ kg, how many bags are needed?

$\text{(A)}\ 36 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 53 \qquad \text{(D)}\ 70 \qquad \text{(E)}\ 71$

Solution

Problem 4

$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}$ is equal to

$\text{(A)}\ \frac{15}{8} \qquad \text{(B)}\ 1\frac{3}{14} \qquad \text{(C)}\ \frac{11}{8} \qquad \text{(D)}\ 1\frac{3}{4} \qquad \text{(E)}\ \frac{7}{8}$

Solution

Problem 5

Which one of the following gives an odd integer?

$\text{(A)}\ 6^2 \qquad \text{(B)}\ 23-17 \qquad \text{(C)}\ 9\times 24 \qquad \text{(D)}\ 96\div 8 \qquad \text{(E)}\ 9\times 41$

Solution

Problem 6

In $\Delta ABC$, $\angle B = 72^{\circ}$. What is the sum, in degrees, of the other two angles?

$\text{(A)}\ 144 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 108 \qquad \text{(D)}\ 110 \qquad \text{(E)}\ 288$

Solution

Problem 7

If the numbers, $\frac{4}{5}$, $81\%$, and $0.801$ are arranged from smallest to largest, the correct order is

$\text{(A)}\ \frac{4}{5}, 81\%, 0.801 \qquad \text{(B)}\ 81\%, 0.801, \frac{4}{5} \qquad \text{(C)}\ 0.801, \frac{4}{5}, 81\% \qquad \text{(D)}\ 81\%, \frac{4}{5}, 0.801 \qquad \text{(E)}\ \frac{4}{5}, 0.801, 81\%$

Solution

Problem 8

The average of $10$, $4$, $8$, $7$, and $6$ is

$\text{(A)}\ 33 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 10 \qquad \text{(E)}$ 7

Solution

Problem 9

André is hiking on the paths shown in the map. He is planning to visit sites A to M in alphabetical order. He can never retrace his steps and he must proceed directly from one site to the next. What is the largest number of labelled points he can visit before going out of alphabetical order?

$\text{(A)}\ 6 \qquad \text{(B)}\ 7 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 13$

Solution

Problem 10

In the diagram, line segments meet at $90^{\circ}$ as shown. If the short line segments are each $3$ cm long, what is the area of the shape?

$\text{(A)}\ 30 \qquad \text{(B)}\ 36 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 45 \qquad \text{(E)}\ 54$

Solution

Part B: Each correct answer is worth 6 points

Problem 11

The floor of a rectangular room is covered with square tiles. The room is 10 tiles long and 5 tiles wide. The number of tiles that touch the walls of the room is

$\text{(A)}\ 26 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 46 \qquad \text{(E)}\ 50$

Solution

Problem 12

Five students named Fred, Gail, Henry, Iggy, and Joan are seated around a circular table in that order. To decide who goes first in a game, they play "countdown". Henry starts by saying "34", with Iggy saying "33". If they continue to count down in their circular order, who will eventually say "1"?

$\text{(A)}\ Fred \qquad \text{(B)}\ Gail \qquad \text{(C)}\ Henry \qquad \text{(D)}\ Iggy \qquad \text{(E)}\ Joan$

Solution

Problem 13

In the diagram, the percent of small squares that are shaded is

$\text{(A)}\ 9 \qquad \text{(B)}\ 33 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 56.25 \qquad \text{(E)}\ 64$

Solution

Problem 14

Which of the following is an odd integer, contains the digit $5$, is divisible by $3$, and lies between $12^2$ and $13^2$?

$\text{(A)}\ 105 \qquad \text{(B)}\ 147 \qquad \text{(C)}\ 156 \qquad \text{(D)}\ 165 \qquad \text{(E)}\ 175$

Solution

Problem 15

A box contains $36$ pink, $18$ blue, $9$ green, $6$ red, and $3$ purple cubes that are identical in size. If a cube is selected at random, what is the probability that it is green?

$\text{(A)}\ \frac{1}{9} \qquad \text{(B)}\ \frac{1}{8} \qquad \text{(C)}\ \frac{1}{5} \qquad \text{(D)}\ \frac{1}{4} \qquad \text{(E)}\ \frac{9}{70}$

Solution

Problem 16

The graph shown at the right indicates the time taken by five people to travel various distances. On average, which person travelled the fastest?

$\text{(A)}\ Alison \qquad \text{(B)}\ Bina \qquad \text{(C)}\ Curtis \qquad \text{(D)}\ Daniel \qquad \text{(E)}\ Emily$

Solution

Problem 17

In a "Fibonacci" sequence of numbers, each term beginning with the third, is the sum of the previous two terms. The first number in such a sequence is $2$, and the third term is $9$. What is the eighth term in the sequence?

$\text{(A)}\ 34 \qquad \text{(B)}\ 36 \qquad \text{(C)}\ 107 \qquad \text{(D)}\ 152 \qquad \text{(E)}\ 245$

Solution

Problem 18

The results of the hair colour of $600$ people are shown in this circle graph. How many people have blonde hair?

$\text{(A)}\ 30 \qquad \text{(B)}\ 160 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 200 \qquad \text{(E)}\ 420$

Solution

Problem 19

What is the area, in $m^2$, of the shaded part of the rectangle? $\text{(A)}\ 14 \qquad \text{(B)}\ 28 \qquad \text{(C)}\ 33.6 \qquad \text{(D)}\ 56 \qquad \text{(E)}\ 42$

Solution

Problem 20

The first 9 positive odd integers are placed in the magic square so that the sum of the numbers in each row, column and diagonal are equal. Find the value of A + E.

$\text{(A)}\ 32 \qquad \text{(B)}\ 28 \qquad \text{(C)}\ 26 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 16$

Solution

Part C: Each correct answer is worth 8 points

Problem 21

A game is played on the board. In this game, the player can move three places in any direction (up, down, right or left) and then can move two places in a direction perpendicular to the first move. If a player starts on S, which position on the board (P, Q, R, T, or W) cannot be reached through any sequence of moves?

$\text{(A)}\ P \qquad \text{(B)}\ Q \qquad \text{(C)}\ R \qquad \text{(D)}\ T \qquad \text{(E)}\ W$

Solution

Problem 22

Forty-two cubes with $1$ cm edges are glued together to form a solid rectangular block. If the perimeter of the base of the block is $18$ cm, then the height, in cm, is

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ \frac{7}{3} \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4$

Solution

Problem 23

$JKLM$ is a square. Points P and Q are outside the square such that triangles JMP and MLQ are equilateral. The size, in degrees, of angle $PQM$ is

$\text{(A)}\ 10 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 25 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 150$

Solution

Problem 24

Five holes of increasing size are cut along the edge of one face of a box as shown. The number of points scored when a marble is rolled through that hole is the number above the hole. There are three sizes of marbles: small, medium and large. The small marbles fit through any of the holes, the medium fit only through holes 3, 4, and 5, and the large fit only through hole 5. You may choose up to 10 marbles of each size to roll and each rolled marble goes through a hole. For a score of 23, what is the maximum number of marbles that could have been rolled?

$\text{(A)}\ 12 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 14 \qquad \text{(D)}\ 15 \qquad \text{(E)}\ 16$

Solution

Problem 25

In a softball league, after each team has played every other team 4 times, the total accumulated points are: Lions 22, Tigers 19, Mounties 14, and Royals 12. If each team received 3 points for a win, 1 point for a tie and no points for a loss, how many games ended in a tie?

$\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 10$

Solution

See also

1999 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources)
Preceded by
1998 CEMC Gauss (Grade 7) 		Followed by
2000 CEMC Gauss (Grade 7)
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
CEMC Gauss (Grade 7)
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1999_CEMC_Gauss_(Grade_7)_Problems&oldid=246707"